GATE-2018 (24) :Wyllie – Time average equation

CSIR-NET 2013

84. A confined aquifer is 40m thick and 8km wide. Two observation wells A and B are located one km apart in the direction of flow. The head in well A is 100m, and the head in well B is 92m. The hydraulic conductivity is 1.0 m/day. Which one of the following presents the total daily flow of water through the aquifer?

A) 5,210 m^3 /day

B) 3,200 m^3 /day

C) 4,800 m^3 /day

D) 2,560 m^3 /day

solution

Darcy law based on the observations that the flow

 rate through a porous medium is proportional to the 

cross-sectional area perpendicular to the flow and is

 also proportional to the head loss per unit length in 

the direction of flow.

Q = K*A*h_L /L

K–hydraulic conductivity = 1.0 m/day

A – aquifer area = 40*8000m = 320000m

h_{L –} hydraulic grade line = 100m – 92m = 8m

L -length (A to B) = 1000m

there fore , 

Q = 1.0 * 320000 * 8 / 1000

Q = 320 * 8

flow rate Q = 2,560 m³ /day